I haven't seen the movie but Loki as know Odin just as long as Thor. Plus Loki also knows how Thor thinks. They don't call him the master of lies for nothing.

Yes, Loki should be able to fool most. Even Heimdall's gaze can't penetrate his illusions and despite that Odin is their father it seems like both of them has mainly seen the authority figure. I think Frigga was the more loving parent.

I also like how Thor finally isn't fooled by the illusions when he goes to talk to Loki in the dungeons but in the end Loki shows that he's still the trickster god.